The analyses I saw separated right wing, left wing, and Islamist.

That doesn’t surprise me at all. Islamic radicals aren’t that different in belief system from a lot of Christian nationalists.

We have all seen family portraits where people pose with American flags, bibles, and guns.

American Christians talk about how the woman/wife is subservient to the husband, how women should stay at home and forego a career and perform traditional roles at home. Many denounce and try to restrict contraceptive access. Many insist that women should/should not dress a certain way.

American Christian talk about how being gay is a sin and how America is a Christian country, not a secular democracy, how we need to have the Ten Commandments in school and in government buildings.

American Christians even grow beards, wear tactical/military-style gear, and drive pickup trucks just like Islamic radicals! (Okay that last one is a a half-joke but it’s kind of funny how the similarities bleed into the aesthetic).

If it looks like a duck, walks like a duck, quacks like a duck…

It's the Left that: - is against Israel - supports Hamas - is against neocons and meddling in the Middle-East - is anti-free speech - is fanatically religious in their beliefs that have no base in reality and are cheering on the death (professional cancelling or real) of the people who dare to disagree with their delusion - are antiscience (antibiology, for one) - are for mutilation of children

The list can be continued.

My point is that classifying Islamists as right-wing is an attempt to gaslight people, to lie to them, is purposefully misleading. Context and public perception matter.